Motor controller for position sensorless drives

ABSTRACT

A system includes a permanent magnet motor having a rotor and a stator. The rotor and the stator have a configuration that causes the motor to generate a back-electromagnetic force (EMF) waveform that is substantially sinusoidal. The system also includes a motor controller having a sliding-mode observer configured to identify the back-EMF waveform and a position observer configured to estimate at least one characteristic of the motor using the identified back-EMF waveform. The stator may include multiple teeth projecting towards the rotor and multiple conductive windings, where each conductive winding is wound around a single tooth. The rotor may include multiple magnetic poles, where each magnetic pole has a span of about 60° or less. The sliding-mode observer may be configured to receive current measurements associated with three-phase signals and voltage commands generated by the motor controller. The position observer may include a proportional-integral (PI) regulator.

CLAIM OF PRIORITY UNDER 35 U.S.C. §120

This application claims the priority and benefit under 35 U.S.C. §120 ofnon-provisional application Ser. No. 13/761,041, entitled “PERMANENTMAGNET MOTOR WITH SINUSOIDAL BACK-EMF WAVEFORM AND RELATED MOTORCONTROLLER FOR POSITION SENSORLESS DRIVES,” filed Feb. 6, 2013(TI-72887), issued as U.S. Pat. No. ______ on ______, the entirety ofwhich is incorporated herein by reference.

TECHNICAL FIELD

This disclosure is generally directed to motors and motor controllers.More specifically, this disclosure is directed to a permanent magnetmotor with a sinusoidal back-electromagnetic force (EMF) waveform and arelated motor controller for position sensorless drives.

BACKGROUND

A permanent magnet motor represents a type of motor where a fixed statorcauses rotation of a movable rotor. The rotor typically includesmultiple magnets embedded in or connected to the rotor, and the statortypically includes multiple conductive windings. Electrical signalsthrough the windings generate a rotating magnetic field that interactswith the magnets of the rotor, causing the rotor to rotate.

“Sensorless” motor control refers to an approach where one or morecharacteristics of a motor, such as motor speed or rotor position, aremathematically derived. Sensorless motor control typically avoids theuse of separate speed and position sensors that are mechanicallyattached to a motor, which might otherwise detrimentally affect theperformance of the motor (such as by affecting the maximum torque outputper volume and drive system reliability).

SUMMARY

This disclosure provides a permanent magnet motor with a sinusoidalback-electromagnetic force (EMF) waveform and a related motor controllerfor position sensorless drives.

In a first example, a system includes a permanent magnet motor having arotor and a stator. The rotor and the stator have a configuration thatcauses the motor to generate a back-electromagnetic force (EMF) waveformthat is substantially sinusoidal. The system also includes a motorcontroller having a sliding-mode observer configured to identify theback-EMF waveform and a position observer configured to estimate atleast one characteristic of the motor using the identified back-EMFwaveform.

In a second example, an apparatus includes a permanent magnet motorhaving a rotor and a stator. The rotor includes multiple magnetic poles,and the stator includes multiple teeth projecting towards the rotor andmultiple conductive windings. The rotor and the stator are configured sothat the permanent magnet motor generates a back-electromagnetic force(EMF) waveform that is substantially sinusoidal.

In a third example, an apparatus includes a motor controller configuredto generate signals for controlling operation of a permanent magnetmotor. The motor controller includes a sliding-mode observer and aposition observer. The sliding-mode observer is configured to identify aback-electromagnetic force (EMF) waveform associated with the permanentmagnet motor. The position observer is configured to estimate at leastone characteristic of the permanent magnet motor using the identifiedback-EMF waveform.

Other technical features may be readily apparent to one skilled in theart from the following figures, descriptions, and claims.

BRIEF DESCRIPTION OF THE DRAWINGS

For a more complete understanding of this disclosure and its features,reference is now made to the following description, taken in conjunctionwith the accompanying drawings, in which:

FIG. 1 illustrates an example system with a permanent magnet motor inaccordance with this disclosure;

FIGS. 2A through 7B illustrate example design details of a permanentmagnet motor in accordance with this disclosure;

FIGS. 8 through 10 illustrate example design details of a motorcontroller for a permanent magnet motor in accordance with thisdisclosure; and

FIG. 11 illustrates an example method for sensorless control of apermanent magnet motor in accordance with this disclosure.

DETAILED DESCRIPTION

FIGS. 1 through 11, discussed below, and the various examples used todescribe the principles of the present disclosure in this patentdocument are by way of illustration only and should not be construed inany way to limit the scope of the disclosure. Those skilled in the artwill understand that the principles of the present disclosure may beimplemented in any suitable manner and in any type of suitably arrangeddevice or system.

FIG. 1 illustrates an example system 100 with a permanent magnet motorin accordance with this disclosure. As shown in FIG. 1, the system 100includes a power supply 102, an inverter 104, and a permanent magnetmotor 106. The power supply 102 represents a direct voltage (DC) powersource that provides DC power to the inverter 104. The power supply 102includes any suitable structure for providing DC power, such as one ormore batteries, fuel cells, solar cells, or other DC source(s).

The inverter 104 receives the DC power from the power source 102 andconverts the DC power into an alternating voltage (AC) form. In thisexample, the inverter 104 represents a three-phase inverter thatconverts DC power into three-phase AC powers that are provided to themotor 106. The inverter 104 includes any suitable structure forconverting power from DC form to AC form. For example, the inverter 104could include a number of transistor switches driven using pulse widthmodulation (PWM) signals.

The motor 106 represents a permanent magnet motor that operates usingthe voltages provided by the inverter 104. As described in more detailbelow, the motor 106 includes a rotor with magnets embedded in orconnected to the rotor. The motor 106 also includes a stator withmultiple teeth around which conductive windings are wound. The windingsare selectively energized and de-energized based on the signals from theinverter 104, which creates a rotating magnetic field that causes therotor to rotate. Also as described in more detail below, the motor 106generates a back-electromagnetic force (EMF) waveform that issubstantially more sinusoidal in form than conventional permanent magnetmotors.

A motor controller 108 controls the operation of the inverter 104 tothereby control the operation of the motor 106. For example, the motorcontroller 108 could generate PWM signals that drive the transistorswitches in the inverter 104. By controlling the duty cycles of the PWMsignals, the motor controller 108 can control the three-phase voltagesprovided by the inverter 104 to the motor 106.

In this example, the motor controller 108 receives as input a commandedspeed signal ω_(e)*, which identifies a desired speed of the motor 106.The motor controller 108 may also receive as input feedback from one ormore observers (such as those implemented within the motor controller108), where the feedback identifies the estimated motor speed, rotorposition, or other characteristic(s) of the motor 106. The motorcontroller 108 uses the inputs to generate PWM signals for driving thetransistor switches in the inverter 104.

As described in more detail below, the motor controller 108 supports theuse of sensorless field-oriented control. That is, the motor controller108 does not receive sensor measurements from sensors mounted in or onthe motor 106. Rather, the motor controller 108 infers one or morecharacteristics of the motor 106, such as motor speed or rotor position.Moreover, the motor controller 108 is designed to operate with the moresinusoidal back-EMF waveform that is generated by the motor 106. Tosupport these functions, the motor controller 108 uses a cascadedobserver-based estimation algorithm to identify position and velocityestimates for the motor 106, even in noisy environments.

In general, the performance of conventional sensorless motor drives isoften limited at low speeds due to a low signal-to-noise (SNR) ratio ofthe back-EMF signals generated by the motors. This may not be acceptablein various applications, such as in industrial applications involvingthe use of electric bikes, robots, or variable-speed compressors.Designing the motor 106 to provide an improved sinusoidal back-EMFwaveform and designing an appropriate control algorithm for the motorcontroller 108 can help to improve the low-speed operation of the motor106 and provide better sensorless drive performance, even in very noisyenvironments.

Various benefits can be obtained using this approach, although theparticular benefits depend on the specific implementation. For example,the motor controller 108 can achieve improved low-speed sensorlessperformance with a simpler hardware design. As described below, only twocurrent sensors may be needed in the motor control algorithm, reducingthe size and cost of using this approach. Moreover, this approach iscompatible with other enhanced algorithms used in field-oriented controldesigns, such as initial position estimation using high-frequency signalinjection (as described in U.S. Pat. No. 5,559,419). Additional detailsregarding the designs of the motor 106 and the motor controller 108 areprovided below.

The components 102-108 here could reside within or otherwise form atleast a part of any suitable larger system 110 that uses one or moremotors. For example, the larger system 110 could represent a vehicle,electric scooter or bicycle, HVAC (heating, ventilation, and airconditioning) system, pump, actuator, compressor, robot, or optical discdrive of a computing device or home entertainment device. In general,any device or system that uses a motor that can operate (eithertemporarily or permanently) at a low speed could incorporate the designsof the motor 106 and the motor controller 108 described in this patentdocument.

Although FIG. 1 illustrates one example of a system 100 with a permanentmagnet motor, various changes may be made to FIG. 1. For example,various components in FIG. 1 could be combined or further subdivided. Asa particular example, one or more of the components 102, 104, 108 couldbe incorporated into the motor 106 itself.

FIGS. 2A through 7B illustrate example design details of a permanentmagnet motor in accordance with this disclosure. These design detailscould be incorporated into the permanent magnet motor 106 in the system100 of FIG. 1. Of course, these design details could be incorporatedinto other permanent magnet motors operating in other systems.

FIGS. 2A and 2B illustrate portions of a rotor 202 and a stator 204 in apermanent magnet motor. As shown here, the rotor 202 includes an outerring or other area having alternating magnetic poles, such as poles206-208. For example, the poles 206 could represent magnetic “north”poles, and the poles 208 could represent magnetic “south” poles. Thesepoles 206-208 can be created in the rotor 202 in any suitable manner.For instance, the poles 206-208 could be created using one or moremagnetic structures embedded in or connected to the rotor 202. As aparticular example, the rotor 202 could include individual magnets,where each magnet forms a single one of the poles 206-208. As anotherparticular example, the rotor 202 could include a ring where individualsections are magnetized in different ways. Any other suitablestructure(s) could be used to provide the alternating magnetic poles206-208. The rotor 202 could be formed from any suitable material(s) andin any suitable manner.

The stator 204 in this example includes multiple teeth 210 that arearranged around the rotor 202 and that project inward from an outer ringtowards the rotor 202. Although not shown here, conductive windings areplaced around the teeth 210 of the stator 204. These conductive windingsare selectively energized and de-energized based on electrical signals,such as those from the inverter 104. This creates a rotating magneticfield that interacts with the magnetic poles 206-208 of the rotor 202,causing the rotor 202 to rotate. Each tooth 210 of the stator 204 canhave any suitable size, shape, and dimensions. The stator 204 itselfcould also be formed from any suitable material(s) and in any suitablemanner.

In a motor such as that shown in FIGS. 2A and 2B, the geometric designof the rotor 202 and stator 204 can be used to create a back-EMFwaveform that is dependent on the rotor's position and speed. Thisback-EMF waveform is caused by periodic changes of magnetic fluxes onthe rotor 202 (where the magnetic fluxes are induced by the movement ofthe magnets that create the poles 206-208 in the rotor 202). As shown inFIG. 2A, when the centerline of a stator tooth 210 is aligned with thecenterline of a magnetic pole 206 or 208 of the rotor, the tooth 210 inthe stator 204 can have the greatest magnetizing flux. As shown in FIG.2B, when the centerline of the stator tooth 210 is aligned with theinter-polar space between two magnetic poles 206-208 of the rotor, thetooth 210 in the stator 204 can have only a small amount of leakagemagnetizing flux. Ideally, the spatial distribution of the magnetic fluxis a nearly triangular waveform as shown in FIG. 3A, which would resultin a nearly trapezoidal back-EMF waveform as shown in FIG. 3B.

Unfortunately, many conventional sensorless motor controllers performposition and velocity estimation calculations based on the assumptionthat the back-EMF waveform will be purely sinusoidal. As a result, theseapproaches may not be effective when used with permanent magnet motors,which typically have back-EMF waveforms that are far from sinusoidal.

This disclosure provides a permanent magnet motor design that utilizesthe “flux leakage effect” to provide a better sinusoidal back-EMFwaveform. As can be seen in FIG. 2B, some magnetic flux enters or leaksinto the stator teeth 210 when the centerlines of the stator teeth 210are aligned with the inter-polar spaces between the rotor's magneticpoles 206-208. This flux leakage is what leads to a change ofmagnetizing flux and the shape of the back-EMF waveform. By detectingthe back-EMF waveform from current measurements, this type of motor issuitable for sensorless control.

A permanent magnet motor can therefore be designed as follows to providean improved sinusoidal back-EMF waveform. First, some conventionalpermanent magnet motors use distributed conductive windings on the teeth210 of a stator 204 as shown in FIG. 4A. In this example, there arethree windings 402-406, and each winding 402-406 is wound around a pairof the stator teeth 210. These conductive windings 402-406 are labeled“A,” “B,” and “C” to indicate that they are energized using differentthree-phase voltages from an inverter.

In contrast, FIG. 4B shows concentrated conductive windings (includingwindings 452-456), where each conductive winding 452-456 is wound arounda single stator tooth 210. Again, these conductive windings 452-456 arelabeled “A,” “B,” and “C” to indicate that they are energized usingdifferent three-phase voltages from an inverter. The use of concentratedconductive windings (each wound around a single stator tooth) helps toincrease the influence of flux leakage shown in FIG. 2B. Thus, animprovement of the sinusoidal shape of the back-EMF waveform generatedby the motor is achieved.

Second, some conventional permanent magnet motors have magnetic poleswith large spans on their rotors. In FIG. 4A, for example, there areonly two magnetic poles on the rotor 202, each spanning approximately180°. The span of a magnetic pole is shown in FIG. 5. To help improvethe sinusoidal shape of the back-EMF waveform generated by a motor,magnets 502 on a rotor (or the magnetic poles on the rotor) could span asmaller angle. For instance, in some motors, each magnet 502 (ormagnetic pole) could span an angle of about 60° or less as illustratedin FIG. 4B. As a result, a rotor could include six or moreangularly-spaced magnetic poles, with each magnetic pole having anangular span of about 60° or less.

Third, the magnets or magnetic poles used in a rotor could be magnetizedradially as shown in FIG. 6A or in parallel as shown in FIG. 6B.Parallel magnetization can result in more flux leakage in a motor, whichcan lead to an improved sinusoidal back-EMF waveform. Thus, the use ofparallel magnetization can be used to provide a more sinusoidal back-EMFwaveform.

Using one or more of these design approaches can make the back-EMFwaveform from a motor significantly more sinusoidal. An example of thisis shown in FIGS. 7A and 7B. In particular, FIG. 7A illustrates aback-EMF waveform 702 from a motor designed as shown in FIG. 4A, whichincludes distributed windings and a 180° magnetic pole span. FIG. 7Billustrates a back-EMF waveform 704 from a motor designed as shown inFIG. 4B, which includes concentrated windings and an approximately 60°magnetic pole span. As can be seen here, the back-EMF waveform 704 has ashape that is significantly more sinusoidal than the back-EMF waveform702.

Note that a perfect sinusoidal shape is not required in a back-EMFwaveform. This is meant merely to show that an improved sinusoidalback-EMF waveform can be obtained using the design approaches describedabove. This can help lead to more accurate sensorless position andvelocity estimation calculations.

Although FIGS. 2A through 7B illustrate examples of design details of apermanent magnet motor, various changes may be made to FIGS. 2A through7B. For example, a rotor 202 could include any number of magnetic poles206-208, and a stator 204 could include any number of teeth 210 and anynumber of concentrated windings 452-456. Moreover, the signals shownhere are for illustration only. Other motors having different designparameters may generate different back-EMF waveforms.

FIGS. 8 through 10 illustrate example design details of a motorcontroller for a permanent magnet motor in accordance with thisdisclosure. These design details could be incorporated into the motorcontroller 108 in the system 100 of FIG. 1. Of course, these designdetails could be incorporated into other motor controllers operating inother systems.

The motor controller here supports the use of field-oriented control,which generally includes controlling the voltages provided to a motorwhile representing those voltages with a vector. The motor, as athree-phase time-dependent and speed-dependent system, can betransformed via projection into a two-coordinate time-invariantsynchronous system. The two coordinate axes are referred to as the d andq axes as illustrated in FIG. 10. The motor is controlled by generatingi_(d) ^(e)* and i_(q) ^(e)* current commands for the d and q axes,respectively. The i_(d) ^(e)* current command is used to control themagnetizing flux of the motor, while the i_(q) ^(e)* current command isused to control the motor torque. These current commands are thenconverted to v_(d) ^(e)* and v_(q) ^(e)* voltage commands for the d andq axes, respectively. The v_(d) ^(e)* and v_(q) ^(e)* voltage commandsdefine a voltage vector that is used to generate three-phase voltagesfor the motor.

As shown in FIG. 8, the motor controller includes a combiner 802, whichreceives the commanded speed signal ω_(e)* and an estimated speed signal{circumflex over (ω)}_(e). The estimated speed signal {circumflex over(ω)}_(e) represents feedback identifying an estimate of the motor'sactual speed. The combiner 802 outputs a difference between thesesignals, which identifies the error between the commanded speed signalω_(e)* and the estimated speed signal {circumflex over (ω)}_(e). Thecombiner 802 includes any suitable structure for combining signals.

A speed controller 804 receives the output of the combiner 802. Thespeed controller 804 uses the error identified by the combiner 802 togenerate the current command i_(q) ^(e)* for the motor. The speedcontroller 804 includes any suitable structure for converting a speederror into a current command.

Another combiner 806 combines the current command i_(q) ^(e)* with afeedback signal i_(q) ^(e), which represents a measurement of the actualcurrent in the q axis. The combiner 806 generates an output identifyingthe difference or error between those signals. The combiner 806 includesany suitable structure for combining signals.

A current regulator 808 receives the output of the combiner 806. Thecurrent regulator 808 uses the error identified by the combiner 806 togenerate the voltage command v_(q) ^(e)* for the motor. The currentregulator 808 includes any suitable structure for converting a currenterror into a voltage command.

A third combiner 810 combines the current command i_(d) ^(e)* with afeedback signal i_(d) ^(e), which represents a measurement of the actualcurrent in the d axis. The combiner 810 generates an output identifyingthe difference or error between those signals. The combiner 810 includesany suitable structure for combining signals.

A current regulator 812 receives the output of the combiner 810. Thecurrent regulator 812 uses the error identified by the combiner 810 togenerate the voltage command v_(d) ^(e)* for the motor. The currentregulator 812 includes any suitable structure for converting a currenterror into a voltage command.

A dq/abc unit 814 receives the v_(d) ^(e)* and v_(q) ^(e)* voltagecommands defining the voltage vector and converts the voltage vectorinto three-phase voltage signals v_(a), v_(b), and v_(c). Thesethree-phase voltage signals define the voltages to be applied (to the“A,” “B,” and “C” windings of the stator) during the three phases of themotor 106. Although not shown, the three-phase voltage signals v_(a),v_(b), and v_(c) can be converted into PWM signals for driving thetransistor switches in the inverter 104. The dq/abc unit 814 includesany suitable structure for converting a voltage vector into three-phasevoltage signals.

Two phase current sensors 816 a-816 b capture measurements of thecurrents in two of the three-phase voltage signals. Among other things,the sensors 816 a-816 b capture information used for back-EMF estimation(which is then used to estimate the rotor position and speed). Eachphase current sensor 816 a-816 b includes any suitable structure formeasuring a current.

An abc/dq unit 818 receives the three-phase current measurements fromthe sensors 816 a-816 b and converts the measurements back into the d-qdomain. In doing this, the abc/dq unit 818 generates the feedbacksignals i_(q) ^(e) and i_(d) ^(e), which represent the measurements ofthe actual currents in the q and d axes. The abc/dq unit 818 includesany suitable structure for converting current measurements associatedwith three-phase voltage signals into current measurements associatedwith d-q axes.

As noted above, sensorless motor control derives one or morecharacteristics of a motor, such as motor speed or rotor position,rather than measuring those characteristics directly. To supportsensorless motor control here, the motor controller includes an EMFsliding-mode observer 820 and a position observer 822. The sliding-modeobserver 820 generally operates to estimate the back-EMF waveform of themotor, where both voltage and current information are used to obtain theback-EMF waveform. The sliding-mode observer 820 includes any suitablestructure for identifying the back-EMF waveform of a motor. The positionobserver 822 generally operates to estimate the position of the motor'srotor, and the speed of the motor can then be estimated using the rateof change in the rotor's position. The position observer 822 includesany suitable structure for identifying the position of a rotor.

FIGS. 9A and 9B illustrate example implementations of the sliding-modeobserver 820 and the position observer 822, respectively. With respectto FIG. 9A, the use of a sliding-mode observer is beneficial since itcan have better dynamic performance to reduce system noise and parametervariation, which makes it suitable for EMF estimation (particularlyduring low motor speeds). The sliding-mode observer 820 uses bothvoltage and current information to estimate the EMF waveform.

In some implementations, the dynamic equation of the sliding-modeobserver 820 can be expressed as:

$\begin{matrix}{{\frac{}{t}\begin{pmatrix}\hat{i_{\alpha}^{s}} \\\hat{i_{\beta}^{s}} \\\hat{e_{\alpha}^{s}} \\\hat{e_{\beta}^{s}}\end{pmatrix}} = {{\frac{1}{\hat{L_{s}}}\begin{pmatrix}v_{\alpha}^{s^{*}} \\v_{\beta}^{s^{*}} \\0 \\0\end{pmatrix}} - {\frac{\hat{R_{s}}}{\hat{L_{s}}}\begin{pmatrix}\hat{i_{\alpha}^{s}} \\\hat{i_{\beta}^{s}} \\0 \\0\end{pmatrix}} - {\frac{K_{sm}}{\hat{L_{s}}}\begin{pmatrix}{{sign}( i_{{\alpha\_}{err}} )} \\{{sign}( i_{{\beta\_}{err}} )} \\{{- {{sign}( {\frac{}{t}i_{{\alpha\_}{err}}} )}} \times \hat{L_{s}}} \\{{- {{sign}( {\frac{}{t}i_{{\beta\_}{err}}} )}} \times \hat{L_{s}}}\end{pmatrix}}}} & (1)\end{matrix}$

Here and in FIG. 9A, v_(α) ^(s)* and v_(β) ^(s)* represent the voltagecommands, and i_(α) ^(s) and i_(β) ^(s) represent the measured currents.Also, i_(α) _(—) _(err) and i_(β) _(—) _(err) represent current errorscalculated by two combiners 902 using the i_(α) ^(s) and i_(β) ^(s)measurements, and v_(α) _(—) _(err) and v_(β) _(—) _(err) representvoltage errors calculated by two sliding-mode controllers 904 usingoutputs of the combiners 902. Further, î_(α) ^(s), î_(β) ^(s), ê_(α)^(s), and ê_(β) ^(s) represent estimated currents and EMF voltages in amotor stator-referred stationary αβ frame. The î_(α) ^(s) and î_(β) ^(s)values can be calculated using a computation unit 906, which can performthe calculations shown in FIG. 9A and provide the î_(α) ^(s) and î_(β)^(s) values as feedback to the combiners 902. In addition, the values{circumflex over (R)}_(s) and {circumflex over (L)}_(s) represent theestimated resistance and inductance of the motor, and K_(sm) representsthe gain for the sliding-mode controllers 904. Here, K_(sm) determinesthe estimation bandwidth of the sliding-mode observer 820 (which may beas high as possible).

By manipulating the estimated currents î_(α) ^(s) and î_(β) ^(s) to beequal to the measured currents i_(α) ^(s) and i_(β) ^(s), the EMFvoltage can be expressed as:

ê _(α) ^(s) =K _(sm)sign(î _(α) ^(s))   (2)

ê _(β) ^(s) =K _(sm)sign(î _(β) ^(s))   (3)

Note that ê_(α) ^(s) and ê_(β) ^(s) are discontinuous waveforms due tothe sliding-mode control. As a result, low-pass filters (LPFs) 908 areused in the sliding-mode observer 820 to obtain continuous EMF vectorsê_(α) _(—) _(lpf) ^(s) and ê_(β) _(—) _(lpf).

With respect to FIG. 9B, knowledge of the back-EMF waveform can be usedto calculate the rotor position of a motor. In conventional sensorlessmotor control algorithms, the rotor's position is often calculated usingan arc-tangent function, and the speed is estimated from thedifferentiation of rotor's position. This can be expressed as:

$\begin{matrix}{\theta_{e} = {{arc}\; {\tan ( \frac{- e_{\alpha}^{s}}{e_{\beta}^{s}} )}}} & (4) \\{\omega_{e} = \frac{\theta_{e}}{t}} & (5)\end{matrix}$

The back-EMF waveform is dependent on the motor speed. However, at verylow speeds, the arc-tangent calculation causes problems when thedenominator in Equation (4) is near zero. This degrades conventionalEMF-based sensorless drive performance because the back-EMF waveform isproportional to the motor speed.

To improve the low speed performance, an observer-based estimationmethod can be used in place of the arc-tangent calculation in theposition observer 822. The position observer 822 in FIG. 9B receives|ê_(q) ^(e)| and ê_(d) ^(e) signals, which can be defined as:

|{circumflex over (e)}_(q) ^(e)|=√{square root over (ê_(α) _(—) _(lpf)^(s) ² +ê _(β) _(—) _(lpf) ^(s) ² )}=ω_(e)λ_(pm)   (6)

ê_(d) ^(e)≈ω_(e)λ_(pm)θ_(err)   (7)

These values represent the estimated EMF voltages in the motorrotor-referred synchronous frame. The position of the motor can then beestimated based on the position error from the back-EMF voltage in theestimated dq reference frame as follows:

$\begin{matrix}\begin{matrix}{\begin{bmatrix}{\hat{e}}_{d}^{r^{\prime}} \\{\hat{e}}_{q}^{r^{\prime}}\end{bmatrix} = {\begin{bmatrix}{\cos \; {\hat{\theta}}_{e}} & {\sin \; {\hat{\theta}}_{e}} \\{{- \sin}\; {\hat{\theta}}_{e}} & {\cos \; {\hat{\theta}}_{e}}\end{bmatrix}\begin{bmatrix}{\hat{e}}_{{\alpha\_}1{pf}}^{s} \\{\hat{e}}_{{\beta\_}1{pf}}^{s}\end{bmatrix}}} \\{= {\begin{bmatrix}{\cos \; {\hat{\theta}}_{e}} & {\sin \; {\hat{\theta}}_{e}} \\{{- \sin}\; {\hat{\theta}}_{e}} & {\cos \; {\hat{\theta}}_{e}}\end{bmatrix}\begin{bmatrix}{{- \omega_{e}}\lambda_{pm}\sin \; \theta_{e}} \\{\omega_{e}\lambda_{pm}\cos \; \theta_{e}}\end{bmatrix}}} \\{= {\begin{bmatrix}{{- \omega_{e}}\lambda_{pm}\sin \; \theta_{err}} \\{\omega_{e}\lambda_{pm}\cos \; \theta_{err}}\end{bmatrix}( {\theta_{err} = {{\hat{\theta}}_{e} -_{\theta \; e}}} )}}\end{matrix} & (8)\end{matrix}$

It can be observed that these back-EMF waveforms contain spatialinformation.

To implement this functionality, the position observer 822 in FIG. 9Bincludes a division unit 950, which scales the ê_(d) ^(e) signal usingthe |ê_(q) ^(e)| signal. The position observer 822 also implements aproportional-integral (PI) regulator using a proportional controller 952and an integral controller 954-956. A combiner 958 combines the outputsof the proportional controller 952 and the integral controller 954-956.The output of the combiner 958 is provided to a scaling unit 960 and anintegrator 962, which generate the estimated velocity {circumflex over(ω)}_(m) and the estimated position {circumflex over (θ)}_(e) of therotor.

Due to the use of a PI regulator, the position observer 822 has alow-pass filter property. As a result, high frequency noise (especiallyat low speeds) is reduced during the estimation. In FIG. 9B, K_(p) andK_(i) represent the proportional and integral controller gains for theposition observer 822, and P represents the pole pairs of the motor.

The components shown in FIGS. 9A and 9B could be implemented using anysuitable structure(s). For example, each of the components 902-908,950-962 could be implemented using hardware modules. In other systems,various input signals could be digitized, and the components 902-908,950-962 could be implemented using software or firmware instructionsexecuted on a hardware platform. A combination of these approaches couldalso be used, where some of the components 902-908, 950-962 areimplemented using only hardware and others of the components 902-908,950-962 are implemented using software/firmware executed by hardware.

Although FIGS. 8 through 9B illustrate examples of design details of amotor controller for a permanent magnet motor, various changes may bemade to FIGS. 8 through 9B. For example, various components in FIGS. 8through 9B could be combined or further subdivided.

Using the designs above for the motor 106 and the motor controller 108,significant improvement can be obtained in the control of the permanentmagnet motor 106, particularly at low speeds. According to experimentalresults with particular implementations of the motor 106 and the motorcontroller 108, a 2% rated speed under full-load operation can beachieved in a permanent magnet motor that provides a substantiallysinusoidal back-EMF waveform. Note, however, that the design of themotor described above could be used without the design of the motorcontroller described above (and vice versa).

FIG. 11 illustrates an example method 1100 for sensorless control of apermanent magnet motor in accordance with this disclosure. As shown inFIG. 11, a permanent magnet motor is obtained at step 1102. Thepermanent magnet motor can have the design as described above, includinga stator with multiple teeth and concentrated conductive windings and arotor with magnetic poles each spanning about 60° or less with parallelmagnetization. Signals for operating the motor are generated at step1104. This could include, for example, the motor controller 108generating three-phase signals for controlling the inverter 104, whichprovides electrical signals to the conductive windings of the motor 106.Because of the design of the motor 106, the motor 106 generates asubstantially sinusoidal back-EMF waveform during its operation at step1106.

During the operation of the permanent magnet motor, currents in thesignals for operating the motor are measured at step 1108. This couldinclude, for example, using the phase current sensors 816 a-816 b tomeasure the currents in two of the three-phase signals. The back-EMFwaveform of the motor is identified using a sliding-mode observer atstep 1110. This could include, for example, the sliding-mode observer820 receiving the measured currents and voltage commands generatedduring operation of the motor 106. This could also include thesliding-mode observer 820 generating continuous EMF vectors using thoseinputs. The position and velocity of the motor are estimated using theidentified back-EMF waveform at step 1112. This could include, forexample, the position observer 822 identifying the estimated positionand velocity of the rotor in the motor 106 using the continuous EMFvectors from the sliding-mode observer 820. Feedback is generated forcontrolling the motor at step 1114. This could include, for example, themotor controller 108 generating speed and current errors using theestimated velocity and the measured currents. The speed and currenterrors can be used to modify the signals for operating the motor.

Although FIG. 11 illustrates one example of a method 1100 for sensorlesscontrol of a permanent magnet motor, various changes may be made to FIG.11. For example, while shown as a series of steps, various steps in FIG.11 could overlap, occur in parallel, occur in a different order, oroccur any number of times. As a particular example, steps forcontrolling the motor occur during operation of the motor and thegeneration of the substantially sinusoidal back-EMF waveform.

While this disclosure has described certain examples and generallyassociated methods, alterations and permutations of these examples andmethods will be apparent to those skilled in the art. Accordingly, theabove description of the examples does not define or constrain thisdisclosure. Other changes, substitutions, and alterations are alsopossible without departing from the spirit and scope of this disclosure,as defined by the following claims

What is claimed is:
 1. A motor controller comprising: a sliding-modeobserver configured to estimate a back-EMF waveform of a magnet motorbased on an estimated current and a current received by the magnet motorfor generating the back-EMF waveform; and a position observer coupledwith the sliding-mode observer, the position observer including: a firstintegrator coupled with the sliding-mode observer, and configured togenerate an integral output based on an integral controller gain and acontinuous EMF vector related to the estimated back-EMF waveform; and asecond integrator coupled with the first integrator, and configured togenerate an estimated position of the magnet motor by integrating aproportion of the integral output.
 2. The motor controller of claim 1,wherein the sliding-mode observer includes: a combiner configured togenerate a current error by comparing the current received by the magnetmotor with the estimated current; and a sliding-mode controller coupledwith the combiner, and configured to estimate the back-EMF waveformbased on the current error.
 3. The motor controller of claim 2, whereinthe sliding-mode controller is configured to estimate the back-EMFwaveform based on a sliding-mode bandwidth and a sign function of thecurrent error.
 4. The motor controller of claim 2, wherein: thesliding-mode observer includes a computation unit coupled with thesliding-mode controller; and the computation unit is configured togenerate the estimated current based on the estimated back-EMF waveform,an estimated resistance of the magnet motor, and an estimated inductanceof the magnet motor.
 5. The motor controller of claim 2, wherein: thesliding-mode observer includes a low-pass filter coupled with thesliding-mode controller; and the low-pass filter is configured to filterthe estimated back-EMF waveform to generate the continuous EMV vector.6. The motor controller of claim 1, wherein: the continuous EMF vectorincludes an estimated q-axis back-EMF waveform and an estimated d-axisback-EMF waveform; the position observer includes a divisional unitcoupled with the sliding-mode observer, and configured to scale theestimated d-axis back-EMF waveform with the estimated q-axis back-EMFwaveform to generate a scaled version of the continuous EMF vector; andthe first integrator is coupled with the sliding-mode observer via thedivisional unit and configured to generate the integral output based onthe integral controller gain and the scaled version of the continuousEMF vector.
 7. The motor controller of claim 1, wherein: the positionobserver includes a combiner coupled with the first integrator; and thecombiner is configured to generate an estimate speed of the magnet motorbased on the integral output and a proportional gain of the positionobserver.
 8. The motor controller of claim 7, wherein the secondintegrator is coupled with the combiner and configured to generate theestimated position by integrating the estimated speed of the magnetmotor.
 9. A motor controller comprising: a sliding-mode observerconfigured to receive a feedback current corresponding to aback-electromagnetic force (EMF) waveform generated by a magnetic motor,the sliding-mode observer including: a combiner configured to generate acurrent error by comparing the feedback current with an estimatedcurrent; and a sliding-mode controller coupled with the combiner, andconfigured to estimate the back-EMF waveform based on the current error;and a position observer coupled with the sliding mode observer, theposition observer configured to estimate an angular position of themagnet motor using the estimated back-EMF waveform.
 10. The motorcontroller of claim 9, further comprising: a first current sensorcoupled to detect a first current of a first-phase voltage of athree-phrase voltage signal causing the magnet motor to generate theback-EMF waveform; a second current sensor coupled to detect a secondcurrent of a second-phase voltage of the three-phrase voltage signal;and a current converter coupled with the first and second currentsensors, the current converter configured to convert the first andsecond current in a three-phrase domain to the feedback current in a α-βdomain.
 11. The motor controller of claim 9, wherein the feedbackcurrent includes a α-axis feedback current and a β-axis feedbackcurrent.
 12. The motor controller of claim 9, wherein: the sliding-modeobserver includes a computation unit coupled with the sliding-modecontroller; and the computation unit is configured to generate theestimated current based on the estimated back-EMF waveform, an estimatedresistance of the magnet motor, and an estimated inductance of themagnet motor
 13. The motor controller of claim 9, wherein: thesliding-mode observer includes a low-pass filter coupled with thesliding-mode controller; and the low-pass filter is configured to filterthe estimated back-EMF waveform to generate a continuous EMV vector. 14.The motor controller of claim 9, wherein the position observer includes:a first integrator coupled with the sliding-mode observer, andconfigured to generate an integral output based on an integralcontroller gain and a continuous EMF vector related to the estimatedback-EMF waveform; and a second integrator coupled with the firstintegrator, and configured to generate an estimated position of themagnet motor by integrating a proportion of the integral output.
 15. Themotor controller of claim 14, wherein: the continuous EMF vectorincludes an estimated q-axis back-EMF waveform and an estimated d-axisback-EMF waveform; the position observer includes a divisional unitcoupled with the sliding-mode observer, and configured to scale theestimated d-axis back-EMF waveform with the estimated q-axis back-EMFwaveform to generate a scaled version of the continuous EMF vector; andthe first integrator is coupled with the sliding-mode observer via thedivisional unit and configured to generate the integral output based onthe integral controller gain and the scaled version of the continuousEMF vector.
 16. The motor controller of claim 14, wherein: the positionobserver includes a combiner coupled with the first integrator; and thecombiner is configured to generate an estimate speed of the magnet motorbased on the integral output and a proportional gain of the positionobserver.
 17. The motor controller of claim 16, wherein the secondintegrator is coupled with the combiner and configured to generate theestimated angular position by integrating the estimated speed of themagnet motor.
 18. A motor controller, comprising: a current sensorcoupled to detect a current corresponding to a driving voltage thatcauses a magnet motor to generate a back-EMF waveform; a processorcoupled to the current sensor; a memory, coupled to the processor,storing instructions, which upon implemented by the processor, configurethe processor to: output a voltage command for generating the drivingvoltage; estimate a back-EMF waveform of the magnet motor based on anestimated current and the detected current; generate an integral outputbased on a continuous EMF vector related to the estimated back-EMFwaveform; and generate an estimated position of the magnet motor byintegrating a portion of the integral output.
 19. The motor controllerof claim 18, wherein the processor is configured by the stored andimplemented instructions to: generate a current error by comparing thedetected current with the estimated current; and estimate the back-EMFwaveform based on a sign function of the current error.
 20. The motorcontroller of claim 19, wherein the processor is configured by thestored and the implemented instructions to: generate the estimatedcurrent based on the estimated back-EMF waveform, an estimatedresistance of the magnet motor, and an estimated inductance of themagnet motor.
 21. The motor controller of claim 18, wherein theprocessor is configured by the stored and the implemented instructionsto: filter the estimated back-EMF waveform to generate the continuousEMV vector.
 22. The motor controller of claim 18, wherein: thecontinuous EMF vector includes an estimated q-axis back-EMF waveform andan estimated d-axis back-EMF waveform; and the processor is configuredby the stored and the implemented instructions to: scale the estimatedd-axis back-EMF waveform with the q-axis back-EMF waveform to generate ascaled version of the continuous EMF vector; and generate the integraloutput based on the integral controller gain and the scaled version ofthe continuous EMF vector.
 23. The motor controller of claim 18, whereinthe processor is configured by the stored and the implementedinstructions to: generate an estimate speed of the magnet motor based onthe integral output and a proportional gain; and generate the estimatedposition by integrating the estimated speed of the magnet motor.
 24. Themotor controller of claim 18, wherein the processor is configured by thestored and the implemented instructions to: adjust the voltage commandbased on the estimated velocity of the magnet motor.